norm¶
-
dolfin.fem.norms.
norm
(v, norm_type='L2', mesh=None)¶ Return the norm of a given vector or function.
- Arguments
- v
- a
Vector
or aFunction
. - norm_type
- see below for alternatives.
- mesh
- optional
Mesh
on which to compute the norm.
If the norm type is not specified, the standard \(L^2\) -norm is computed. Possible norm types include:
Vectors
Norm Usage \(l^2\) norm(x, ‘l2’) Default \(l^1\) norm(x, ‘l1’) \(l^\infty\) norm(x, ‘linf’) Functions
Norm Usage Includes the \(L^2\) -term \(L^2\) norm(v, ‘L2’) Yes \(H^1\) norm(v, ‘H1’) Yes \(H^1_0\) norm(v, ‘H10’) No \(H\) (div) norm(v, ‘Hdiv’) Yes \(H\) (div) norm(v, ‘Hdiv0’) No \(H\) (curl) norm(v, ‘Hcurl’) Yes \(H\) (curl) norm(v, ‘Hcurl0’) No Examples of usage
v = Function(V) x = v.vector() print norm(x, 'linf') # print the infinity norm of vector x n = norm(v) # compute L^2 norm of v print norm(v, 'Hdiv') # print H(div) norm of v n = norm(v, 'H1', mesh) # compute H^1 norm of v on given mesh